Of 100 students asked if they like rock and roll or country music, 7 said they like neither, 90 said they like rock and roll, and 57 said they like country music. How many students like both?

Because 7 students said they didn't like either rock or country, that leaves 93 students (100 – 7) who voted for rock, country, or both. If each of the remaining 93 students had been able to vote for either country or rock, but not both, there would have been only 93 votes, but there were 147 more votes cast (90 + 57). The remaining 54 votes (147 – 93) must have been cast as second votes. Therefore, 54 students must have voted twice — once for rock, and once for country.

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Of 100 students asked if they like rock and roll or country music, 7 said they like neither, 90 said they like rock and roll, and 57 said they like country music. How many students like both?